Convergence and error analysis of a bi-quadratic triangular galerkin finite element model for heat conduction simulation

Sulaeman, Erwin and Hoq, S.M. Afzal and Okhunov, Abdurahim and Hilmy, Irfan and Badran, Marwan A A (2019) Convergence and error analysis of a bi-quadratic triangular galerkin finite element model for heat conduction simulation. Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, 54 (1). pp. 78-86. ISSN 2289-7879

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Abstract

Present paper elaborates solution of partial differential equations (PDE) of two dimensional steady state heat conduction by using a bi quadratic triangular Galerkin’s finite element method (QGFEM). The steady state heat distribution is modeled by a two-dimensional Laplace partial differential equations. A six-node triangular element model is developed for the QGFEM based on quadratic basis functions on the Cartesian coordinate system where physical domain is meshed by structured grid. The elemental stiffness matrix is formulated by using a direct integration scheme along the triangular domain area without the necessity to use the Jacobian matrix. Validation is conducted to an analytical solution of a rectangular plate having mixed, asymmetric boundary conditions. Comparisons of the present QGFEM results and the exact solution show promising results. The convergence of the method is presented by checking the error analysis for various number of elements used for the simulation

Item Type:	Article (Journal)
Additional Information:	6427/67603
Uncontrolled Keywords:	Bi-quadratic triangular finite element model, Galerkin method, error analysis, heat conduction, partial differential equation
Subjects:	T Technology > TJ Mechanical engineering and machinery > TJ255 Heat engines
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Engineering Kulliyyah of Engineering > Department of Manufacturing and Materials Engineering Kulliyyah of Engineering > Department of Mechanical Engineering
Depositing User:	Dr Erwin Sulaeman
Date Deposited:	18 Feb 2019 10:14
Last Modified:	12 Jul 2019 16:50
URI:	http://irep.iium.edu.my/id/eprint/67603

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